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Gröbner bases and products of coefficient rings

2002; Cambridge University Press; Volume: 65; Issue: 1 Linguagem: Inglês

10.1017/s0004972700020165

1755-1633

Graham H. Norton, Ana Sălăgean,

Commutative Algebra and Its Applications

Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A [ x 1 ,…, x n ] can be easily obtained by ‘joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor.